What is the integral from 0 to infinity of e^{(t-2)x} ?

The integral from 0 to infinity of e^{(t-2)x} is -1/(t-2)

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integral from 0 to infinity of e^{(t-2)x}

\int_{0}^{\infty} e^{(t - 2) x} d x

- \frac{1}{t - 2}

Solution steps

\int_{0}^{\infty} e^{(t - 2) x} d x

Compute the indefinite integral:

\int e^{(t - 2) x} d x = \frac{1}{- 2 + t} e^{(- 2 + t) x} + C

Compute the boundaries:

\int_{0}^{\infty} e^{(t - 2) x} d x = 0 - \frac{1}{- 2 + t}

= 0 - \frac{1}{- 2 + t}

Simplify

= - \frac{1}{t - 2}

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What is the integral from 0 to infinity of e^{(t-2)x} ?
The integral from 0 to infinity of e^{(t-2)x} is -1/(t-2)